Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
172 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. #17984143 | C4 | semidirect |
| 11. C4⋊#11764040 | C4 | semidirect |
| 14. C4⋊C8×C137 | C4 | semidirect |
| 62. C137 | #1300 | semidirect |
| 71. C4⋊C8 | #10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14555520 | 2 |
| #22578339 | 2 |
| #22577459 | 2 |
| #1300 | 137 |